Validation of convection-limited cooling of samples for freeze-fracture electron microscopy

Rapid freezing is the most important step in sample preparation for freeze-fracture and other cryotechniques for electron microscopy. A simple heat transfer model is experimentally validated to show that convection from the cryogen to the specimen is the limiting step in rapid freezing of small samples [Biot modulus, (hd/k) less than 1] by measuring cooling rates in a variety of samples, materials, and cryogens. In comparison to the commonly accepted conduction-limited model, the convection-limited model predicts, and our experiments show, that cooling rates are proportional to the surface area to volume ratio, independent of the sample thermal conductivity, and inversely proportional to the product of sample density and heat capacity. We show that almost any material can be frozen at similar rates if the sample thickness, the cryogen, and the method and velocity of contact with cryogen are similar. Liquid ethane or propane cooled to liquid nitrogen temperature are shown to give the best results.